JPS59224913A - Adaptive linear forecasting method - Google Patents

Abstract

PURPOSE:To accelerate the converging speed of forecast calculation by constituring so as to attain effective forecast by the algorithm based on a method correcting a coefficient at every reception of a data, so-called on-line identification method. CONSTITUTION:Let a filter be a P-order linear forecasting filter, then a forecast error epsiloni in using data of i-sample (1<=i<p) is expressed as Equation (1). The LMS algorithm 4 is used as an algorithm minimizing the square mean value epsiloni<2> formed from this epsiloni. As shown in Equation (2) clearly, the epsiloni<2> is the i- variable function of the weight coefficient Cj. The maximum gradient method is used to obtain a Cj minimizing the epsiloni<2>. That is, the coefficient Cj is rewritten by means of the correcting algorithm in Equation (3). The degree of effect of a coefficient Ci.j on the epsiloni<2>, i.e., the sensitivity to coefficient is defined as Equation (4), l-set of DELTA<k> is selected in the order of larger one (1<l<i) and coefficients with a low coefficient sensitivity are not corrected, then the converging speed is accelerated.

Description

TECHNICAL FIELD The present invention relates to an adaptive linear prediction method, and more particularly, to an adaptive linear prediction method configured to efficiently predict a signal using an adaptive filter. It is something.

Prior Art Conventional prediction methods use filters with constant coefficients, which has the disadvantage that it is difficult to predict non-stationary signals.

In addition, in the past, there have been various methods of adaptive prediction algorithms, and although they have better prediction effects than fixed filters, many of them have the disadvantage of slow convergence speed of prediction calculations.

Purpose The present invention was made in order to eliminate the above-mentioned drawbacks of the conventional technology, and it is possible to make effective predictions using an algorithm based on the so-called online identification method, which modifies coefficients each time data is received. The purpose of this paper is to provide an adaptive linear prediction method configured as follows.

Example Hereinafter, the present invention will be described in detail based on the drawings.

FIG. 1 is a block diagram of a filter showing one embodiment of the present invention.

In FIG. 1, the reference numeral 1 is a one-sample delay device, the reference numeral 2 is a variable coefficient multiplier, and the reference numeral 3 is an adder.

Now, consider the case where a discrete signal sequence X(k) is input.

Assuming that the filter in FIG. 1 is a second-order linear prediction filter, the prediction error εi when using i samples of data (1≦p) is t r =x(1<)−c
j x (k j ) −・−−・・(1))=
=1.

The LMS algorithm indicated by reference numeral 4 is used as an algorithm for minimizing the root mean square ε generated from the above εi.

However, "-" means an unsample average.

As is clear from equation (2), ε is a one-variable function of the weighting coefficient Cj.

The maximum slope method is used to find cj at which the rock is at its minimum. That is, the coefficient cjO is rewritten using a correction algorithm according to the following equation. However, k in equation (3) is a parameter related to convergence speed and stability.

However, when the maximum slope method according to equation (3) is used, as the optimum coefficient value approaches, that is, as the number of corrections increases, the slope of the evaluation function leap becomes gentler, and the coefficient cj,
The convergence of i to the optimal value cji may become slow in this vicinity. Therefore, the number of trials or trial time is
Grow and move.

Therefore, the degree of influence of the coefficient cj,t on ε,
In other words, if the coefficient sensitivity is defined as kl, t coefficients (1<#<i) with large Δ' are selected, and coefficients with low coefficient sensitivity are not modified, the convergence speed can be increased. can.

FIG. 2 is a flowchart representing an algorithm for selecting a modified coefficient in the above method.

This flowchart is included in the L, M, S algorithm of FIG.

Then, in step A3, 1( is incremented by 1).

If Ak) is larger than ml, the process returns to step A3.

From now on, repeat the same operation to obtain a coefficient with low coefficient sensitivity (+
++A) Select from t larger coefficients at t, and stop control as coefficients lower than me are not modified.

1x1 indicates the absolute value of X.

In addition, in the prediction methods described so far, p-order measurements have been the basis, but if the statistical properties of the input signal do not change, m-order measurements (m<p) may be sufficient. It's also possible.

] Therefore, calculate 6m (m=1,...p), and then calculate , 7iI > Shimori middle story; Ki......Nakara... When filling (5), the prediction is m
I'll stop until the next one.

If this prediction order truncation method is used, it is even faster,
It can be converged.

FIG. 3 is a flowchart representing the algorithm of the above prediction order truncation method. In step S1, 4(
m=1,... p). m in step S2
Assign 0 to . In step S3, the value of m is increased by 1. In step S4, the inkstone bow at m obtained in step S3 is compared, and if 弔:>aF, the process returns to step S3.

On the other hand, if ε crystal is ε6, then formula (5) is established, and the process ends.

EffectsAs is clear from the above explanation, it is possible to perform fast and effective signal prediction by using an adaptive filter for linear prediction and also using the correction coefficient truncation method and the prediction order truncation method. Effects can be obtained.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing an embodiment of the present invention, Fig. 2 is a flowchart showing an algorithm for selecting correction coefficients in the correction coefficient truncation method, and Fig. 3 is an algorithm for the prediction order truncation method. FIG. , Lido...Sample delay device 2...Variable coefficient multiplier 3...
・Adder. Patent applicant: Canon Co., Ltd. Figure 2 Figure 3

Claims (1)

[Claims] An adaptive linear prediction method that uses an adaptive filter to abort modified cases at low sensitivity areas to speed up the convergence of prediction calculations.